Stochastic phase space formulation and non-potential interactions

A recently developed formulation of quantum mechanics is described, which is based on the idea of localizing particles in stochastic phase space. This approach, which even in relativistic domain, adheres strictly to the probability interpretation of quantum mechanics, is shown to bypass all the conventional problems of relativistic quantum mechanics - such as the theory not admitting a conserved probability current or being unstable against small perturbations. Our formalism generates a quantization procedure which is applicable both to relativistic and non-relativistic systems, however, the interactions involved automatically become non-local and non-potential in nature. The theory is applied to quantize a classical model of a spin-1/2 charged particle in an external electromagnetic field. The energy levels for such a system are studied and the entire hydrogen spectrum including Lamb shift effects are shown to be reproduced. Implications of the theory for the short-distance structure of space-time are discussed